Okay, in this section here, we're going to talk about some applications. And the first one is the average value. The arithmetic average is the sum of all values divided by the number of values. Okay, an example of that would be a test score where my average is 80, my average is 90. And one of the way or not one of the ways the way that we find this is his number one, we add all the values up. Then we divide the sum of all values by the number of values.

And that's, and then we get our answer. So I give you an example. Here it says find the average value of temperature readings the last four days. So day one was 76 degrees. Day 272 day 382 day 488. Okay, so first thing we're gonna do is we're gonna find the sum of all these and we add them up 7672 82 and 88, we get our answer 318.

And then we divide that by the number of values, the number of values here are 41234. There they are. And so we divide 318 by the number of values of four, and our average value is 79.5. So what we can say here is that the average value of the temperature reading the last four days was 79.5 degrees. All right, so let's clear off the slides. And let's go to the next one.

And what we're going to do here is find the average value of the following test scores. Now what I'm going to do is I'm going to show you how to do this by using a calculator. Alrighty, and I've written the solution up here, but I'm going to show you how to use a calculator to do that. Now the calculator that I'm going to use is the one that's part of the Windows operating system. Alrighty, so let's do that right now. Okay, here I have my calculator.

And again, it's part of the Windows operating system. I'm in standard mode. There's scientific but standard mode will do fine here for what we want. And so I'm going to add these numbers up right here. Alright, so I'm going to add up 94% plus 89% 79% 98% and 65%. And that equals, well for 25.

We can see here and I did it right here. Now, the only thing I need to do is divide by five, because I have 12345 numbers. So I hit the divide. And I'm going to hit the five and I'm going to say equals 85. So the average value here of all these, the sum of all these percentages of I take the average It's 85%. Okay, so these are test scores, the student has done five of them, we need to give him a grade at the end of the section.

So we average these test scores up and he gets 85%. Alrighty, so let's stop here for a minute. I'm going to go to the next slide. The next slide has some problems for you to do, I suggest you you find a calculator. Again, you can use the one in the Windows operating system and give it a shot. Okay, I'm going to stop here, and we're going to go to the next slide.

Okay, here I gave you three problems, there are probably going to be some more. I have. This is the end of the section by the way. We've got one more topic here. And then we're ending this section. We're going to go to the next section which talks about negative numbers.

But this one is the last one here again in section one. So, I'm going to give you a worksheet with some more problems on all the topics that we have presented here in the first section. Alright, so getting back to this, take a few minutes and here they are. I want you to find the average value of those of those problems, this three of them here, and stop. If you have to stop the presentation. Find the answers.

And then when you continue the next slide, I give you the answers. Okay, again, I'm not harping on this too much anymore, but there's a help number. And if you don't want that, then you can contact me through the This website and I, I'll help you out, we can set something up. Again, if I have enough students, I enough demand I will do a some type of online tutoring section or tutoring class. And what I'll do is I'll make an announcement at some point, you'll get an email and then we'll see how many people would like would like to take advantage of that. All right, I'm going to stop this.

You're going to do the problems here. And then when you click back on, you'll see the answers. Okay, here are the answers. And take a look at them. If you have any problems, you know what to do. All right, the next section we're going to talk about is RMS.

And then again, we have finished with this first Section. Okay, in this application, we're going to look at the RMS value. And the RMS value is a specific way that we determine the voltage of an AC waveform in electrical or electronics. And that's really the only thing I want to say right here. If you take my course understanding voltage, current and resistance, I go into that a little bit more. And if you take some electronic courses from me again, if that section we need to define what an AC voltage is, again, we'll, we'll derive that a little bit more but but right here, we're just looking at the mathematics.

And so I'm showing you the mechanics of how we find an RMS value of an AC waveform. Alright, so again, we're looking for the RMS value and RMS stands for root mean square. And it's actually three different operations, which I show you down here. And if you look at it, even though I'm stating RMS right there, the way we do our operations, it's actually in reverse, we find the square the mean and the root. So, let's, let's go to it and explain the first one. One other thing I'm going to mention here is mean and average are the same thing.

If I want to find the mean of a group of numbers, I want to find the average of a group of numbers, okay? So again, meaning average means the same thing. So the first thing we're going to do is we're going to square each value. Okay? Then we're going to find the average value of the square And then we're going to take the root of the average value here. Let's go through this and you'll see what I mean.

Okay, so I give you an example here. And I say, find the RS RMS value of 234. What's the first thing we want to do? We want to square each value. All right? So when I say square each value, okay, let's take the first one to a square is a number multiplied by itself.

So we have four. So what is that? two squared is two times two to two times two is four. The square of three is three times three, which is nine, which is right there. And the square of four is four times four, which is 16. All right, so I've just done step one.

Now step two All right, find the average value of the squares. Okay, so I'm going to take the average. So what do we do from the last section? What do we do? We add up our numbers. So we're adding up four plus nine plus 16.

Okay? And we're going to divide that by the number of entries or the number of numbers. In this case, we have three. So what do I get when I do that? 9.67. That's the average value of the squares.

All right, so what do I want to do? I want to take the root or the square root of the average value. The square root of nine dot six, seven is three dot one one. So that is my answer. So what I say is the RMS value here, equals three dot one, one That's my RMS value. So the RMS value of 234 is three dot one, one.

All right, let's clear the slide and look at another one here. Okay, let's find the value, the RMS value of this 6779 8977 87.5. Now what I'm going to do here now is I again, I'm going to show you how to do this using a calculator. All right, and then you're going to do the ones in the bottom here. And then when I hit the continue button, I have the answers for you. Okay, we're going to find the RMS value here.

And here are my numbers that I want to start off with right there. group of numbers I'm gonna find RMS. Again, I'm using the calculator in the Windows operating system. So let's start. So the first thing I want to do is I want to square each number. Alright?

And I'm going to add them, because I'm the next step is the mean. All right. So let's look at what happens here. First number 67 squared. All right, plus 79.5 squared plus 89 squared plus 77. squared plus 87 dot five five squared. Okay, now notice before I hit the equal sign, it kind of shows you right here, what's going on.

So you can kind of track yourself. So look at i squared 67 squared 79 dot five squared 89 squared 77 and then i squared the last 187 dot five. Now I'm okay. And then what do I have to do? I got to find out what that equals I and then I did that's my I'm finding my mean, sort of find my mean. I take the sum of all numbers which I have here, and I divided by what the number of values 12345.

Let me get that back. 12345 so I'm going to divide by five equals. Bingo. Okay, bingo. Now what's the last thing I want to find the root or the square root? All I do is hit my radical sign right there.

There it is. There's my answer. My answer here is at will go to two decimal places at 404. So what I can say here is the RMS value for this Let me get my thing here. My pointer is at DOT four zero. All right, that's my answer.

All right at four zero. And let's just double check that I, I'm looking at this here. And let's see. Yep, at 400 right there. Okay, we're going to go to two decimal places. So 8040 there's my answer.

I use the calculator. All right. So, what I'd like you to do now is do these three here. Stop the presentation, do them and then click the Go button or click the button. menu button on your computer, and you will see the answers. Alright, here are the answers to the problems right there.

And if you have any problems, you have my help number, you know how to get ahold of me. Look at the previous explanation again and see if you can get them but there they are right here. All right. Now this ends section one, and we're going, the next section will be section two. And we're going to be starting on two negative numbers. And we're going to keep on going here.

So if you have any problems again, give me a call. Send me an email. See in section two